How to rearrange


with $x$ as the subject?

Is this possible?

I'm struggling to work out how I should go about this.

I also tried putting it into wolfram alpha to check how it was worked out but it doesn't return a result.


1 Answer 1


As seen here, it is generally impossible to solve for $x$ given a particular $y$, so I doubt you would have much luck solving for $x$ for general $y\in\mathbb Q$. The only closed form solution for rational $y$ occurs at $(0,0)$...

One may, however, approximate the solution using Newton's method:

Let us define $x_n$ as follows:


Then as $n\to\infty$, $x_n\to x$ is our solution. For example, with $y=1$ and $x_0=0$, we get the following:





And thus we have our solution:


  • $\begingroup$ It's not true that the only closed form solution occurs at $(0,0)$. For example, for $y = 2+\sin(1)$ the solution is obviously $x=1$. $\endgroup$ Mar 3, 2017 at 23:30
  • $\begingroup$ @RobertIsrael I meant for $y\in\mathbb Q$, sorry. For other $y$ with arguments about what is closed form and what is not, please make comments under the linked question (it would be most useful there) $\endgroup$ Mar 3, 2017 at 23:31

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.